The Solution of Crack Problems by Using Distributed Strain Nuclei

1996 ◽  
Vol 210 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A M Korsunsky ◽  
D A Hills
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problems ◽  
The Relationship ◽  
Distributed Strain

Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.

Analysis of Branched Cracks

1978 ◽  
Vol 45 (4) ◽  
pp. 797-802 ◽  
Author(s):  
K. K. Lo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Complex Form ◽  
Function Technique ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Potential Formulation ◽  
Crack Problems

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.

Harmonic Holes for Nonconstant Fields

1979 ◽  
Vol 46 (3) ◽  
pp. 573-576 ◽  
Author(s):  
G. S. Bjorkman ◽  
R. Richards
Keyword(s):  
Integral Equation ◽  
Stress Concentration ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Maximum Stress ◽  
Internal Boundary ◽  
Parametric Form ◽  
Original Field ◽  
Hole Boundary

Hole shapes which do not perturb the first invariant of the stress tensor of an isotropic stress field with superimposed linear gradients are derived. These haromonic holes, called the deloid and cardeloid, result from the solution of a nonlinear singular integral equation and can be expressed very simply in parametric form. A comparison of stresses around the boundary of a deloid with a circular hole of the same size shows that the deloid significantly reduces not only the maximum stress concentration but also the total variation of stress around the hole boundary. Deloids and cardeloids without internal boundary loading exist only in locations where the first invariant of the original field does not change sign.

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